Factorization dynamics and Coxeter-Toda lattices

Details Factorization dynamics and Coxeter-Toda lattices Factorization dynamics and Coxeter-Toda lattices

1999-06-24

arxiv.org/abs/solv-int/9906013v2

Comm. Math. Phys. 212, Issue 2, 297-321 (2000)

Mathematics

Quantum Algebra

33 pages, latex, minor corrections

Scientific paper

10.1007/s002200000212

It is shown that the factorization relation on simple Lie groups with standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can be regarded as a discretization of the Toda flow. In case of $SL_n$ the integrals of the factorization dynamics are integrals of the relativistic Toda system. A substantial part of the paper is devoted to the study of symplectic leaves in simple complex Lie groups, its Borel subgroups and their doubles.

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